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High-resolution two-dimensional NMR spectra ofhalf-integer-spin quadrupolar nuclei from

one-dimensional projectionsT. Vosegaard, D. Massiot

To cite this version:T. Vosegaard, D. Massiot. High-resolution two-dimensional NMR spectra of half-integer-spinquadrupolar nuclei from one-dimensional projections. Chemical Physics Letters, Elsevier, 2007, 437,pp.120-125. �10.1016/j.cplett.2007.01.077�. �hal-00127883�

High-resolution two-dimensional NMR spectra of half-integer-spin quadrupolar

nuclei from one-dimensional projections

Thomas Vosegaard a,*, Dominique Massiot b

a Center for Insoluble Protein Structures (inSPIN), Interdisciplinary Nanoscience Center (iNANO) and Department of

Chemistry, University of Aarhus, DK-8000 Aarhus C, Denmark

b Centre de Recherche sur les Matériaux à Haute Température, CNRS UPR4212 FR2950, 45071 Orléans Cedex 2,

France

* Corresponding author:

Thomas Vosegaard

Center for Insoluble Protein Structures (inSPIN),

Interdisciplinary Nanoscience Center (iNANO) and Department of Chemistry

University of Aarhus

Langelandsgade 140, DK-8000 Aarhus C

Denmark

Email tv@chem.au.dk

Tel +45 8942 3866

Mobile +45 6020 2639

Fax +45 8619 6199

Key-Words: Projection-Reconstruction; Second-order quadrupole interaction; PRODI; Radial

Sampling

Abstract

We present a technique providing high-resolution spectra of quadrupolar nuclei with half-integer

nuclear spin displaying significant second-order linebroadening. The technique, dubbed chemical

shift – quadrupolar projection-reconstruction of one-dimensional spectra (CQ-PRODI) exploits the

different magnetic field dependence of the chemical shift and second-order quadrupolar effect. One-

dimensional spectra recorded at different magnetic field strengths are represented as projections

along different directions in the two-dimensional spectrum that correlates the chemical shift and the

second-order quadrupolar lineshape. We present CQ-PRODI spectra for 27Al in 9Al2O3·2B2O3 and

for 71Ga in β-Ga2O3 which display resolution of all sites in the chemical shift dimension.

Page 2/13

1. Introduction

Solid-state nuclear magnetic resonance (NMR) studies on quadrupolar nuclei with half-integer

nuclear spin provide a wealth of information contributing to the understanding of a host of

compounds ranging from inorganic materials such as ceramics [1] and glasses [2] to biological

macromolecules [3,4]. One of the major challenges in studying half-integer-spin quadrupolar nuclei

is that the typically very strong quadrupole coupling interactions (several MHz) of these nuclei will

cause a significant line broadening of the NMR resonances. Even for the central transition (m=1/2

↔ – 1/2) which is not broadened by the quadrupole interaction to first order, will be broadened by

the second-order quadrupolar effect, a broadening that may only be reduced but not removed by

magic-angle spinning (MAS).

The introduction of dynamic-angle spinning (DAS) [5,6] and double-rotation (DOR) [6,7] as

well as the more recent multiple-quantum MAS (MQMAS) [8] and satellite-transition MAS

(STMAS) [9] techniques have been essential in the past decade’s applications of solid-state NMR

for structural characterization targeting quadrupolar nuclei since they offer high-resolution spectra

by complete removal of the second order lineshape. With these techniques, the high resolution is

achieved, but unfortunately often at the expense of very delicate experimental setup (DOR, DAS,

and STMAS) or low sensitivity (MQMAS).

A complementary approach to improving the resolution for quadrupolar nuclei displaying

second-order broadened resonances is to employ the highest available magnetic field strength since

the second-order quadrupolar effect is inversely proportional to the magnetic field. For example, a

recent study employing magnets with up to 40 T field strengths provided complete resolution of 4

27Al sites in the aluminoborate 9Al2O3·2B2O3 (A9B2) [10], while experiments performed at lower

commercially available field strengths give second-order broadened spectra with significant overlap

of the resonances. At the extreme magnetic field strength of 40 T the linewidth due to drift and field

inhomogeneity exceeds the second-order linewidth and hence the high resolution is achieved at the

expense of the information on the quadrupole coupling interaction.

Page 3/13

In this Letter we demonstrate that it is possible to reconstruct a 2D spectrum correlating the high-

resolution chemical shift with the second-order quadrupolar lineshape, from 1D spectra recorded at

different magnetic field strengths. The technique, dubbed chemical shift – quadrupolar projection-

reconstruction of one-dimensional spectra (CQ-PRODI), may be applied to both spinning and static

sample with a sensitivity comparable to that of a one-dimensional spectrum.

2. Experimental

The 27Al spectra of A9B2 have been acquired under rapid magic-angle spinning (15 to 30 kHz)

using single-pulse excitation with typical recycle delays of 1 s at magnetic fields of 9.4 T to 19.5 T

(400 MHz to 830 MHz 1H Larmor frequency) in stable and homogeneous superconducting magnets

[11], and at magnetic fields of 25 T and 40 T in resistive or hybrid magnets. In the latter case

individual free-induction decays (FIDs) were acquired and referenced independently to correct for

the field-drift between the scans [10]. The 71Ga NMR spectra of β-Ga2O3 were recorded using full-

echo acquisition to obtain pure absorption mode spectra with flat baselines and improved signal-to-

noise ratios [12]. All 1D spectra were processed on the spectrometer and, if necessary, corrected for

distorted baselines by piecewise spline interpolation of the baseline regions using SIMPSON

[13,14]. Projection-reconstructions of the 2D CQ-PRODI spectra were also performed using

SIMPSON by normalizing all spectra and subsequently following the reconstruction procedure

applied for SLF-PRODI [15].

3. Results and discussion

--- Figure 1 here ---

Projection-reconstruction techniques have recently been introduced to reduce the dimensionality

of a variety of liquid-state [16,17] and solid-state [15,18] NMR experiments. In a more general

Page 4/13

scope we can remark that while most of the multidimensional experiments are acquired by time-

consuming stepwise increment of each evolution time, there exist several examples of

reconstruction methods that rely on other degrees of freedom of the system: heteronuclear dipolar

scaling factor in SLF-PRODI [15], spinning angle in VACSY [19] or DACSY [20] experiments,

pitch encoding in PASS [21] or QPASS [22] experiments, spatial or orientational encoding in one-

pulse acquisition schemes [23,24], spinning sidebands of MAS spectra in TOP processing [25,26].

We will apply the PRODI technique to quadrupolar nuclei by taking advantage of the fact that the

strength of the chemical shift interaction is proportional to the external magnetic field, while the

second-order quadrupolar effect is inversely proportional to the external magnetic field. Bearing

this in mind, we may regard the spectrum of a quadrupolar nucleus at a given magnetic field as

being a projection with a given angle in a 2D chemical-shift – quadrupolar correlation spectrum.

For illustration Fig. 1a shows a series of 27Al spectra of A9B2. In Fig. 1b these spectra are

represented in the 2D spectrum, and the scales have been arbitrarily chosen such that the B0 = 17.5

T spectrum forms an angle of 45º with the quadrupolar axes. A spectrum recorded at an other

magnetic field strength (B0’) will be represented by an angle of arctan((B0’/B0)2). For example, 9.4-

T and 25-T spectra will correspond to projections at angles of 16° and 63°, respectively, as shown

in Fig. 1b. The corresponding projections are shown as contour plots in Fig. 1c. By combining these

2D projections we can reconstruct the 2D CQ-PRODI spectrum providing the desired chemical-

shift/quadrupolar correlation. We note that the different field dependence of the chemical shift and

second-order quadrupolar effect has previously been exploited in the spectral interpretation, e.g.,

using a so-called discontinuity multifield graph [12,27] or a second-order graphic extrapolation

diagram [11,28]. We also note that the TOP representation for half-integer quadrupolar nuclei

[25,26] allows a separation of the second-order lineshapes for the central and individual satellite

transitions which may be represented as different projections in a CQ-PRODI spectrum.

A9B2 contains one tetrahedrally coordinated Al site (AlIV), two different penta coordinated Al

sites (AlV(1) and AlV(2)), and one octahedrally coordinated Al site (AlVI) with double occupancy and

Page 5/13

hence double intensity in the NMR spectra [11]. Even at the high field strength of 25 T (Fig. 1a)

there is still a slight overlap of AlIV with one of the AlV sites and a significant overlap between the

two AlV sites, while a spectrum recorded at 40 T displays complete resolution of the four sites [10].

The 2D CQ-PRODI spectrum resulting from projections from spectra recorded at six different

magnetic field strengths from 9.4 T to 40 T is represented in Fig. 1d with the quadrupolar axis

corresponding to a 9.4-T spectrum. The spectrum displays the expected four resonances, and the

horizontal slices through these resonances (Fig. 1e) show the second-order lineshapes for these four

sites. As expected these lineshapes have their leftmost singularity situated close to zero since the

horizontal slices are not influenced by the chemical shift of the particular resonance in a CQ-

PRODI spectrum. A comparison of the second-order quadrupolar lineshapes of the four resonances

with the lineshapes simulated employing previously determined parameters [11] (Fig. 1f) shows

good overall agreement while in particular the two AlV sites show distortions. These artefacts

appear due to the heavy overlap between these two sites in all spectra displaying a second-order

quadrupolar lineshape for these two sites.

The resolution achieved in the chemical shift dimension of the CQ-PRODI spectrum depends on

resolution of the 1D spectrum from the highest magnetic field strength used for the reconstruction,

and since the 1D 40-T spectrum was employed to achieve the CQ-PRODI spectrum in Fig. 1 it is

not surprising that a resolution of all four sites was achieved. To cope with spectra of lower

resolution, and in the case of A9B2 to employ spectra only from todays commercially available

range of superconducting magnets, we have performed a large number of numerical simulations of

CQ-PRODI spectra and have come to the conclusion that the chemical-shift projections are always

free of second-order lineshape and only contain a Gaussian/Lorentzian-like lineshape. Being

equipped with the chemical shift projection with Gaussian/Lorentzian peaks rather than peaks with

second-order quadrupolar lineshapes is interesting, since it opens for the possibility to cautiously

apply resolution enhancement techniques to the chemical shift projection. Among many resolution

Page 6/13

enhancement techniques, we have found that the MaxEnt algorithm with multiple search directions

[29] as implemented for NMR purposes by Hoch and Stern [30] is the most stable for our purposes.

--- Figure 2 here ---

This procedure is illustrated in Fig. 2 for 27Al in A9B2, and Fig. 2a shows the CQ-PRODI

spectrum obtained from 1D spectra at a number of magnetic field strengths from 9.4 T to 25 T. In

this spectrum we observe the presence of four patterns of which those corresponding to the AlV sites

are heavily overlapping as also observed in the chemical-shift projection in Fig. 2b, and overall this

projection does not improve the resolution compared to the 25-T spectrum (Fig. 1a), but as

mentioned above the resonances now show a Gaussian/Lorentzian lineshape. Figure 2d shows the

chemical shift projection (Fig. 2b) after it has been subjected to a MaxEnt deconvolution with a 6-

ppm Lorentzian point-spread function. We may use the deconvoluted chemical shift projection to

improve the resolution in the 2D CQ-PRODI spectrum by adding it as a horizontal projection in a

refined reconstruction of the CQ-PRODI spectrum. Figure 2c shows the horizontal projection from

the deconvoluted spectrum in Fig. 2d, and the CQ-PRODI spectrum resulting from projections of

the 1D spectra recorded at magnetic field strengths between 9.4 T and 25 T and horizontal

projection is shown in Fig. 2e. This spectrum is comparable to the one in Fig. 1c, and is superior to

the resolution of the 25-T spectrum. We furthermore note that the slices through the four resonances

display second-order quadrupolar lineshapes (not shown) are virtually identical to those reported in

Fig. 1d.

--- Figure 3 here ---

--- Table 1 here ---

Page 7/13

A very useful feature of CQ-PRODI spectra is that their chemical shift projection display

resonances at the position of the isotropic chemical shift while regular 1D spectra show

displacements from the isotropic chemical shifts by the isotropic second-order quadrupolar shift.

Figure 3 shows the 40 T 27Al spectrum of A9B2 (Fig. 3a) along with the 9.4 T to 40 T CQ-PRODI

chemical shift projection (Fig. 3b and Fig. 1c). Table 1 summarizes the peak positions measured in

the 40 T spectrum and in CQ-PRODI spectra achieved using spectra from magnetic fields of 9.4 T –

40 T and 9.4 T – 25 T, respectively. The CQ-PRODI values agree very well with previously

determined chemical shifts [11,31], while we observe that the resonances in the 40 T spectrum are

shifted by up to 3 ppm due to the second-order quadrupolar shift even if the actual second-order

quadrupolar lineshape is masked by the principal field inhomogeneity.

--- Figure 4 here ---

While the MQMAS and STMAS techniques fail for nuclei with large quadrupole couplings due

to low sensitivity in the case of MQMAS [32] and excessive line-broadening for STMAS [33],

there is no such limitation to CQ-PRODI. To investigate this appealing property of CQ-PRODI we

have applied this technique to 71Ga spectra of β-Ga2O3 which contains a GaVI and a GaIV site with

quadrupole couplings of 8.3 MHz and 11.2 MHz, respectively [12,34]. These values are well

beyond the size of the quadrupole couplings amenable to MQMAS or STMAS, and only DAS [27]

and single-crystal NMR [34] have achieved complete resolution of the two sites. Even a regular

MAS spectrum at 9.4 T would result in a second-order lineshape with a width exceeding 70 kHz

implying that a MAS spectrum acquired using a modest spinning rate would result in overlap of the

spinning sidebands [12,27,35] which are very difficult to interpret and to model and would be very

difficult to handle with CQ-PRODI. To circumvent this problem we decided to use CQ-PRODI on a

series of static 71Ga spectra of β-Ga2O3, recorded at magnetic field strengths of 7.1 T, 9.4T, 11.7 T,

and 18.8 T as illustrated in Fig. 4. The CQ-PRODI reconstruction of the four 1D spectra, shown in

Page 8/13

Fig. 4e, suggests the presence of two sites, but the sum projection along of the chemical shift

dimension reveals a strong overlap of the resonances for these sites.

The strong overlap in the CQ-PRODI spectrum is partly ascribed to the larger linewidth of the static

second-order lineshape compared to the MAS lineshape. For the MAS lineshape the outer

singularities appear at frequencies of a)6(2 2MASmin ην +−= and a2

712MAS

max )1( ην −−= , where

and 02 4/3 νν Qa = ))12(4/( −= IICQQν . For a static sample these values are a)1(16Stat

min ην +−=

and a2Statmax )3( ην += , and hence it may easily be established that the width of the static second-

order lineshape exceeds that of the MAS lineshape by factors of 2.4 – 3.4 depending on the

asymmetry parameter, η, leading to significantly increased overlap in static spectra than in MAS

spectra. While this increased overlap is an obvious challenge to CQ-PRODI, the form of the static

second-order lineshape allows establishing a horizontal projection. This was not possible for MAS

lineshapes which only reside on one side of the zero frequency, but becomes possible for static

lineshapes which spread over positive and negative values around the zero frequency. Hence we

may use the chemical shift trace at zero frequency in the quadrupolar dimension of the CQ-PRODI

spectrum (indicated by a dashed line in Fig. 4e) as a horizontal projection, leading to the improved

CQ-PRODI spectrum in Fig. 4f. In this spectrum the appearance of two sites is very clear from the

sum projection of the chemical shift dimension which displays significantly improved resolution

when compared to the projection in Fig. 4e.

To further improve the resolution of the static CQ-PRODI spectrum, we use the MaxEnt

deconvolution strategy and add a horizontal MaxEnt deconvoluted projection of the chemical shift

sum projection (Fig. 4f) to yield the final 2D CQ-PRODI spectrum in Fig. 4g. The chemical shift

projection from this spectrum displays two resonances located at 29 ± 33 ppm (GaVI) and 232 ± 33

ppm (GaIV), respectively, where the error limits represent ¼ of the FWHH linewidths. These

chemical shifts compare reasonably well with our previous high-precision measurements of 25 ± 1

ppm and 196 ± 2 ppm from single-crystal NMR [34], although the match is not perfect. An obvious

reason for this is that the static lineshapes are influenced by the chemical shift anisotropies (CSA)

Page 9/13

which amount to 37 ppm (GaVI) and -33 ppm (GaIV) [34] and thereby add to the linewidths and may

shift the resonance position in the chemical shift dimension of the CQ-PRODI spectrum. The CSA

broadening in the chemical shift dimension of the CQ-PRODI spectrum will increase proportionally

with the magnetic field strength suggesting that at some point there will no longer be a gain in

resolution by adding projections from static spectra recorded at higher magnetic fields. This

happens when the line broadening from the CSA exceeds that of the second-order quadrupolar

lineshape which would at approximately 24 T for GaVI and 40 T for GaIV.

Most half-integer quadrupolar nuclei display appreciable CSAs so the CSA broadening will be a

pronounced problem (of growing importance at higher magnetic fields) for many cases when

applying static experiments to reconstruct the CQ-PRODI spectrum. This fact favors the use of

MAS experiments for CQ-PRODI even in cases where the second-order lineshape exceeds the

spinning frequency. In these cases we suggest the use of infinite spinning speed reconstructions

from QPASS experiments [22] which displays the appreciated line narrowing by MAS and

furthermore eliminate any contributions from the CSA.

4. Conclusions

In conclusion, we have presented the CQ-PRODI technique which employs 1D static or MAS

experiments of half-integer quadrupolar nuclei to reconstruct a high-resolution 2D spectrum

correlating the chemical shift in one dimension with the second-order quadrupolar lineshape in the

other dimension. By applying MaxEnt resolution enhancement in the data processing, CQ-PRODI

spectra of considerably better resolution than the original 1D spectra may be achieved. Furthermore,

the CQ-PRODI spectra compensate for the second-order quadrupolar shift in the high-resolution

dimension allowing determination of isotropic chemical shift. The CQ-PRODI spectra display

sensitivities comparable with 1D spectra making CQ-PRODI an obvious candidate for achieving

high-resolution spectra of quadrupolar nuclei in samples with low sensitivity. Such cases include

Page 10/13

low-γ nuclei and nuclei with low natural abundance of the relevant isotope or samples with low

abundance of the nucleus in question, e.g., metals in metal binding sites of proteins.

Acknowledgment

Support from the Danish National Research Foundation, the Danish Natural Science Research

Council, CNRS UPR4212, FR 2950, and ANR RMNHRHC is acknowledged. We would like to

thank Prof. Z. Gan and NHMFL Tallahassee, FL, for performing the very-high field experiments at

19.5 T, 25 T, and 40 T.

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Table 1

27Al peak positions in the 40 T single-pulse spectrum of A9B2 and in the chemical shift projections

of the CQ-PRODI spectra.

Peak position (ppm)

Spectrum type Field strength (T) AlVI AlV(1) AlV(2) AlIV Ref.

MASa 40 7(2) 51(2) 42(2) 69(3) [10]

CQ-PRODIa 9.4 – 40 8(2) 53(3) 44(3) 72(3) This work

CQ-PRODIa 9.4 – 25 8(2) 52(3) 40(3) 75(4) This work

DOR / MAS 7 – 17.6 9 52 44 71 [11]

MQMAS 7.1 – 9.4 8(1) 52(1) 44(1) 71(1) [31] aThe numbers in parentheses represent the half width at half height, reflecting accuracy of the measured peak

position.

Page 12/13

Figure captions

Figure 1. (a) 27Al MAS NMR spectra of A9B2 and (b) schematic representation of a two-

dimensional chemical shift – quadrupolar correlation spectrum showing the 27Al spectra from (a) at

orientations according to their magnetic field strengths. (c) Corresponding 2D projections in a 17.5

T chemical shift – quadrupolar correlation spectrum. (d) 2D 9.4-T CQ-PRODI spectrum achieved

from projections from spectra recorded at 9.4 T, 14.1 T, 17.6 T, 19.5 T, 25 T, and 40 T, and (e)

traces through the four resonances in the chemical shift dimension. (f) Simulated second-order

lineshapes based on previously reported parameters [11,31]. Contour levels are drawn at 10%, 20%,

…, 90% of the maximum intensity.

Figure 2. 27Al CQ-PRODI spectrum for A9B2 (a) and corresponding chemical shift projection (b)

achieved using projections from spectra recorded at 9.4 T, 14.1 T, 17.6 T, 19.5 T, and 25 T. MaxEnt

resolution enhanced chemical-shift spectrum (d) and the corresponding projection (c). CQ-PRODI

spectrum resulting from the 1D spectra horizontal projection (e) corresponding chemical shift

projection (f). Contour levels are drawn at 10%, 20%, …, 90% of the maximum intensity.

Figure 3. (a) 40 T 27Al spectrum and (b) chemical-shift projection of the 27Al CQ-PRODI spectrum

of A9B2. The projection is identical to the vertical projection in Fig. 1d. The dashed lines indicate

the isotropic chemical shifts for the four Al sites.

Figure 4. Static 71Ga spectra of β-Ga2O3 recorded at (a) 7.1 T, (b) 9.4 T, (c) 11.7 T, and (d) 18.8 T.

(e) 9.4-T CQ-PRODI spectrum obtained from the four 1D spectra, (f) the same spectrum but with

an additional horizontal projection resulting from the slice at zero in the quadrupolar dimension as

indicated by a dashed line in (e). (g) The same spectrum with an additional horizontal MaxEnt

projection. Contour levels are drawn at 10%, 20%, …, 90% of the maximum intensity.

Page 13/13

Figure 1

Figure 2

Figure 3

Figure 4